It's usually easy to find a Resupply or Reinforce mission in the various sectors blocks. I suggest however to steer clear of Reinforce Missions, they can land up to 3 doffs in sick bay even on a success and they'll be out of commission for 3 days. They also take 5 doffs i think and you can't sent colonists,

Resupply missions are short, 3 hours and they give decent military exp in return, 46 a pop. They only take 2 officers, heck i think you can sent colonists to do these too!

Yeah, resupplies are usually what I steer for, but it seems my find rate on these missions must be lower than yours, as it's usually like a jack pot for me if I find one.

Also what are these 'briefing' missions? Dont think I've come across those.